Op-Amp Practical Parameters

An ideal op-amp has infinite gain and zero offset, but a real LM741 or TL071 does not. These practical imperfections determine whether your precision instrumentation circuit measures a 1 mV thermocouple signal accurately or drowns it in error.

Core Concept

The input offset voltage Vos is the differential DC voltage that must be applied between the inputs to force the output to zero. For the LM741, this is typically 2 mV. In a closed-loop gain of 100, even 1 mV of Vos produces 100 mV of DC error at the output.

The input bias current Ib is the average DC current drawn by both input terminals. The input offset current Ios is the difference between the two bias currents. In circuits with large feedback resistors, Ib flowing through those resistors creates additional voltage error at the input.

The slew rate SR limits how fast the output voltage can change, regardless of signal frequency. The LM741 slews at only 0.5 V/µs. The gain-bandwidth product GBP relates closed-loop gain to usable bandwidth: at a closed-loop gain of 10, the LM741 has only 100 kHz of bandwidth.

Key Equations

Output error due to offset voltage: Vout_error = Vos × (1 + Rf/R1) for an inverting or non-inverting configuration.

Output error due to bias current: Vout_error = Ib × Rf approximately, when source resistance is matched.

Slew rate limit on maximum undistorted sine frequency: fmax = SR / (2π × Vpeak) where SR is in V/s and Vpeak in volts.

Gain-bandwidth product: GBP = Acl × BW. For TL071, GBP = 3 MHz. At Acl = 30, BW = 3 MHz / 30 = 100 kHz.

CMRR in dB: CMRR = 20 × log10(Ad / Acm) where Ad is differential gain and Acm is common-mode gain.

Given:
  Op-amp: LM741
  Slew rate SR = 0.5 V/µs = 0.5 × 10^6 V/s
  Output sine wave peak amplitude Vpeak = 5 V
  Find: maximum frequency for undistorted output

Why this formula:
  Slew rate limits the maximum rate of change of output.
  A sine wave dVout/dt = 2π f Vpeak cos(2πft), max at t=0.
  At the limit: SR = 2π × fmax × Vpeak

Formula:
  fmax = SR / (2π × Vpeak)

Substitution:
  fmax = (0.5 × 10^6) / (2π × 5)

Calculation:
  2π × 5 = 31.42
  fmax = 500,000 / 31.42 = 15,913 Hz

Final Answer:
  fmax ≈ 15.9 kHz
  Above this frequency, the 5 V peak sine wave will be distorted (triangular).

Exam Tip: GATE tests the slew rate formula fmax = SR/(2πVpeak) almost every year. A common mistake is forgetting to multiply by 2π and just dividing SR by Vpeak. Also, CMRR affects common-mode noise rejection, not slew rate. Do not confuse GBP with open-loop gain. At unity gain (Acl = 1), bandwidth equals GBP numerically.

Key Properties

• LM741 has Vos = 2 mV typical and 6 mV maximum at 25°C, making it unsuitable for precision DC amplification without trimming.
• TL071 uses JFET inputs, giving Ib ≈ 30 pA, far lower than the LM741's 80 nA bipolar input stage.
• CMRR of 90 dB means a 1 V common-mode signal produces only 31.6 µV of equivalent differential input error.
• Power supply rejection ratio PSRR tells how much supply noise appears at the output; LM741 PSRR is 96 dB typically.
• GBP = 1 MHz for LM741 means at a closed-loop gain of 100, usable bandwidth is only 10 kHz.
• Output short-circuit protection in the LM741 limits output current to about 25 mA, preventing damage when the output is shorted to ground.
• Modern precision op-amps like the OPA277 have Vos < 10 µV and CMRR > 130 dB, showing how much the LM741 lags behind.

Quick Revision

• Vos: DC offset at input; amplified by closed-loop gain to produce output error.
• Ib: average input current; Ios: difference in bias currents between two inputs.
• SR = 0.5 V/µs for LM741; TL071 has SR = 13 V/µs.
• fmax (slew-limited) = SR / (2π Vpeak).
• GBP = Acl × BW = constant for a given op-amp.
• CMRR = 20 log10(Ad/Acm); higher is better for noise rejection.
• PSRR = how well the op-amp rejects noise on VCC or VEE supply rails.
• Exam trap: students apply GBP to open-loop gain rather than closed-loop gain, getting bandwidth values that are far too large.